Multigrid method nonlinear

Eigure 2 compares the LPM results for the nonlinear Poisson-Boltzmann equation (Eq. 13) and the analytical solutions of the linearized equation (Eq. 35), together with a numerical solution using the multigrid method. The parameters are the bulk ionic molar concentration c o = — 4 M, = c oNa where Na is Avogadro s number, z = 1 is the dielectric constant of the... 

Full Approximation Scheme Nonlinear Multigrid Method... 

For many years the standard preconditioner has been the method of nested factorisation due to [8]. The iteration scheme of choice, based on well known approaches to nonlinear optimisation, has been the orthomin method of [153]. Only recently have there been challenges to nested factorisation from multigrid methods and domain decomposition methods. Deeper analysis may lead to improvements on basic orthomin. (See [134] for a complete overview and [150] for a review of multigrid.)... 

Holst, M., R. E. Kozack, F. Saied and S. Subramaniam. (1994b). Treatment of electrostatic effects in proteins multigrid-based Newton iterative method for solution of the full nonlinear Poisson-Boltzmann equation. Proteins. 18 231-45. 

Treatment of Electrostatic Effects in Proteins—Multigrid-Based Newton Iterative Method for Solution of the Full Nonlinear Poisson-Boltzmann Equation. 

Damanik, H., Hron, J., Ouazzi, A., Turek, S. (2013). Monolithic Newton-multigrid solution techniques for incompressible nonlinear flow models. International Journal for Numerical Methods in Fluids, 71, 208-222. doi 10.1002/fld.3656. 

---